The squashed fuzzy sphere, fuzzy strings and the Landau problem. (English) Zbl 1320.81086
Summary: We discuss the squashed fuzzy sphere, which is a projection of the fuzzy sphere onto the equatorial plane, and use it to illustrate the stringy aspects of noncommutative field theory. We elaborate explicitly how strings linking its two coincident sheets arise in terms of fuzzy spherical harmonics. In the large \(N\) limit, the matrix-model Laplacian is shown to correctly reproduce the semi-classical dynamics of these charged strings, as given by the Landau problem.
MSC:
81T75 | Noncommutative geometry methods in quantum field theory |
81Q20 | Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory |
81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
83E30 | String and superstring theories in gravitational theory |
81V70 | Many-body theory; quantum Hall effect |